feat: add ElasticBands

Author: Aglargil

PathPlanning/ElasticBands/elastic bands.pdf

@@ -0,0 +1,262 @@
+"""
+Elastic Bands
+
+author: Wang Zheng (@Aglargil)
+
+Ref:
+
+- [Elastic Bands: Connecting Path Planning and Control]
+(http://www8.cs.umu.se/research/ifor/dl/Control/elastic%20bands.pdf)
+"""
+
+import numpy as np
+import sys
+import pathlib
+import matplotlib.pyplot as plt
+from matplotlib.patches import Circle
+
+sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
+
+from Mapping.DistanceMap.distance_map import compute_sdf
+
+# Elastic Bands Params
+MAX_BUBBLE_RADIUS = 100
+MIN_BUBBLE_RADIUS = 10
+RHO0 = 20.0  # Maximum distance for applying repulsive force
+KC = 0.05  # Contraction force gain
+KR = -0.1  # Repulsive force gain
+LAMBDA = 0.7  # Overlap constraint factor
+STEP_SIZE = 3.0  # Step size for calculating gradient
+
+# Visualization Params
+ENABLE_PLOT = True
+ENABLE_INTERACTIVE = False
+MAX_ITER = 50
+
+
+class Bubble:
+    def __init__(self, position, radius):
+        self.pos = np.array(position)  # Bubble center coordinates [x, y]
+        self.radius = radius  # Safety distance radius ρ(b)
+        if self.radius > MAX_BUBBLE_RADIUS:
+            self.radius = MAX_BUBBLE_RADIUS
+        if self.radius < MIN_BUBBLE_RADIUS:
+            self.radius = MIN_BUBBLE_RADIUS
+
+
+class ElasticBands:
+    def __init__(self, initial_path, obstacles, rho0=RHO0, kc=0.05, kr=-0.1):
+        self.distance_map = compute_sdf(obstacles)
+        self.bubbles = [
+            Bubble(p, self.compute_rho(p)) for p in initial_path
+        ]  # Initialize bubble chain
+        self.kc = kc  # Contraction force gain
+        self.kr = kr  # Repulsive force gain
+        self.rho0 = rho0  # Maximum distance for applying repulsive force
+
+    def compute_rho(self, position):
+        """Compute the distance field value at the position"""
+        return self.distance_map[int(position[0]), int(position[1])]
+
+    def contraction_force(self, i):
+        """Calculate internal contraction force for the i-th bubble"""
+        if i == 0 or i == len(self.bubbles) - 1:
+            return np.zeros(2)
+
+        prev = self.bubbles[i - 1].pos
+        next_ = self.bubbles[i + 1].pos
+        current = self.bubbles[i].pos
+
+        # f_c = kc * ( (prev-current)/|prev-current| + (next-current)/|next-current| )
+        dir_prev = (prev - current) / (np.linalg.norm(prev - current) + 1e-6)
+        dir_next = (next_ - current) / (np.linalg.norm(next_ - current) + 1e-6)
+        return self.kc * (dir_prev + dir_next)
+
+    def external_force(self, i):
+        """Calculate external repulsive force for the i-th bubble"""
+        h = STEP_SIZE  # Step size
+        b = self.bubbles[i].pos
+        rho = self.bubbles[i].radius
+
+        if rho >= self.rho0:
+            return np.zeros(2)
+
+        # Finite difference approximation of the gradient ∂ρ/∂b
+        dx = np.array([h, 0])
+        dy = np.array([0, h])
+        grad_x = (self.compute_rho(b - dx) - self.compute_rho(b + dx)) / (2 * h)
+        grad_y = (self.compute_rho(b - dy) - self.compute_rho(b + dy)) / (2 * h)
+        grad = np.array([grad_x, grad_y])
+
+        return self.kr * (self.rho0 - rho) * grad
+
+    def update_bubbles(self):
+        """Update bubble positions"""
+        new_bubbles = []
+        for i in range(len(self.bubbles)):
+            if i == 0 or i == len(self.bubbles) - 1:
+                new_bubbles.append(self.bubbles[i])  # Fixed start and end points
+                continue
+
+            f_total = self.contraction_force(i) + self.external_force(i)
+            alpha = self.bubbles[i].radius  # Adaptive step size
+            new_pos = self.bubbles[i].pos + alpha * f_total
+            new_pos = np.clip(new_pos, 0, 499)
+            new_radius = self.compute_rho(new_pos)
+
+            # Update bubble and maintain overlap constraint
+            new_bubble = Bubble(new_pos, new_radius)
+            new_bubbles.append(new_bubble)
+
+        self.bubbles = new_bubbles
+        self._maintain_overlap()
+
+    def _maintain_overlap(self):
+        """Maintain bubble chain continuity (simplified insertion/deletion mechanism)"""
+        # Insert bubbles
+        i = 0
+        while i < len(self.bubbles) - 1:
+            bi, bj = self.bubbles[i], self.bubbles[i + 1]
+            dist = np.linalg.norm(bi.pos - bj.pos)
+            if dist > LAMBDA * (bi.radius + bj.radius):
+                new_pos = (bi.pos + bj.pos) / 2
+                rho = self.compute_rho(
+                    new_pos
+                )  # Calculate new radius using environment model
+                self.bubbles.insert(i + 1, Bubble(new_pos, rho))
+                i += 2  # Skip the processed region
+            else:
+                i += 1
+
+        # Delete redundant bubbles
+        i = 1
+        while i < len(self.bubbles) - 1:
+            prev = self.bubbles[i - 1]
+            next_ = self.bubbles[i + 1]
+            dist = np.linalg.norm(prev.pos - next_.pos)
+            if dist <= LAMBDA * (prev.radius + next_.radius):
+                del self.bubbles[i]  # Delete if redundant
+            else:
+                i += 1
+
+
+class ElasticBandsVisualizer:
+    def __init__(self):
+        self.obstacles = np.zeros((500, 500))
+        self.start_point = None
+        self.end_point = None
+        self.elastic_band = None
+
+        if ENABLE_PLOT:
+            self.fig, self.ax = plt.subplots(figsize=(8, 8))
+            # Set the display range of the graph
+            self.ax.set_xlim(0, 500)
+            self.ax.set_ylim(0, 500)
+
+        if ENABLE_INTERACTIVE:
+            self.path_points = []  # Add a list to store path points
+            # Connect mouse events
+            self.fig.canvas.mpl_connect("button_press_event", self.on_click)
+        else:
+            self.path_points = [
+                [30, 136],
+                [61, 214],
+                [77, 256],
+                [77, 309],
+                [53, 366],
+                [41, 422],
+                [51, 453],
+                [110, 471],
+                [184, 437],
+                [257, 388],
+                [343, 353],
+                [402, 331],
+                [476, 273],
+                [456, 206],
+                [430, 160],
+                [402, 107],
+            ]
+            self.obstacles = np.load(pathlib.Path(__file__).parent / "obstacles.npy")
+            self.plan_path()
+
+        self.plot_background()
+
+    def plot_background(self):
+        """Plot the background grid"""
+        if not ENABLE_PLOT:
+            return
+
+        self.ax.cla()
+        self.ax.set_xlim(0, 500)
+        self.ax.set_ylim(0, 500)
+        self.ax.grid(True)
+        if self.path_points:
+            self.ax.plot(
+                [p[0] for p in self.path_points],
+                [p[1] for p in self.path_points],
+                "yo",
+                markersize=8,
+            )
+
+        self.ax.imshow(self.obstacles.T, origin="lower", cmap="binary", alpha=0.3)
+        if self.elastic_band is not None:
+            path = [b.pos.tolist() for b in self.elastic_band.bubbles]
+            path = np.array(path)
+            self.ax.plot(path[:, 0], path[:, 1], "b-", linewidth=2, label="path")
+
+            for bubble in self.elastic_band.bubbles:
+                circle = Circle(
+                    bubble.pos, bubble.radius, fill=False, color="g", alpha=0.3
+                )
+                self.ax.add_patch(circle)
+                self.ax.plot(bubble.pos[0], bubble.pos[1], "bo", markersize=10)
+
+        self.ax.legend()
+        plt.draw()
+        plt.pause(0.01)
+
+    def on_click(self, event):
+        """Handle mouse click events"""
+        if event.inaxes != self.ax:
+            return
+
+        x, y = int(event.xdata), int(event.ydata)
+
+        if event.button == 1:  # Left click to add obstacles
+            size = 30  # Side length of the square
+            half_size = size // 2
+
+            # Ensure not out of the map boundary
+            x_start = max(0, x - half_size)
+            x_end = min(self.obstacles.shape[0], x + half_size)
+            y_start = max(0, y - half_size)
+            y_end = min(self.obstacles.shape[1], y + half_size)
+
+            # Set the square area as obstacles (value set to 1)
+            self.obstacles[x_start:x_end, y_start:y_end] = 1
+
+        elif event.button == 3:  # Right click to add path points
+            self.path_points.append([x, y])
+
+        elif event.button == 2:  # Middle click to end path input and start planning
+            if len(self.path_points) >= 2:
+                self.plan_path()
+
+        self.plot_background()
+
+    def plan_path(self):
+        """Plan the path"""
+
+        initial_path = self.path_points
+        # Create an elastic band object and optimize
+        self.elastic_band = ElasticBands(initial_path, self.obstacles)
+        for _ in range(MAX_ITER):
+            self.elastic_band.update_bubbles()
+            self.path_points = [b.pos for b in self.elastic_band.bubbles]
+            self.plot_background()
+
+
+if __name__ == "__main__":
+    visualizer = ElasticBandsVisualizer()
+    if ENABLE_PLOT:
+        plt.show()